当函数f(x,y)趋向于极限f(0,0)时,xln(1-y)/(√(2xy+1)-1)
问题描述:
当函数f(x,y)趋向于极限f(0,0)时,xln(1-y)/(√(2xy+1)-1)
答
xln(1-y)/(√(2xy+1)-1)
=xln(1-y)(√(2xy+1)+1)/((2xy+1)-1)
=ln(1-y)(√(2xy+1)+1)/(2y)
所以
极限=lim ln(1-y)(√(2xy+1)+1)/(2y)
=lim -y(1+1)/(2y)
=-1